Log-Domain Arithmetic Coding for Low-Complexity Interval Updates
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Solution Overview
Problem
Existing arithmetic encoding methods face challenges due to limited precision and implementation complexity, particularly in avoiding multiply operations and managing self-adaptive probability estimation, which complicates the encoding process and makes it difficult to implement on personal computers.
Innovation Solution
The method maps arithmetic encoding and decoding operations to the logarithm domain, using add/subtract operations and approximations for interval updates, thereby avoiding complex computations and table look-ups, and simplifying probability updates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If arithmetic encoding is performed using traditional methods with multiply operations and self-adaptive probability estimation, then coding efficiency is improved, but implementation complexity increases and precision is limited
Solution Approach 1:
The patent transforms the arithmetic encoding parameters from linear domain to logarithmic domain. By representing probabilities and interval values in logarithmic form, the multiplication operations are converted to addition operations, which are simpler to implement. This parameter transformation maintains coding efficiency while reducing computational complexity and improving precision.
Solution Approach 2:
The patent replaces complex multiply operations with simpler add/subtract operations in the logarithmic domain. This substitution eliminates the need for complex multiplication hardware or software routines, significantly reducing implementation complexity while maintaining the essential arithmetic encoding functionality.
2Device complexity
If multiply operations are avoided using approximations or look-up tables, then implementation complexity is reduced, but precision and adaptability deteriorate
Solution Approach 1:
By changing to logarithmic domain representation, the patent achieves exact arithmetic operations through addition instead of approximation through lookup tables. The logarithmic transformation allows precise probability updates and interval calculations without relying on pre-computed tables or approximate methods, thereby maintaining high precision while reducing complexity.
3Productivity
If self-adaptive probability estimation is used to improve coding efficiency, then compression ratio is improved, but device complexity and difficulty of implementation increase
Solution Approach 1:
The patent implements self-adaptive probability estimation in the logarithmic domain, where probability updates become simple addition operations. This transformation maintains the adaptability needed for high compression ratios while making the implementation straightforward through basic arithmetic operations, thereby reducing implementation difficulty.
4Device complexity
If arithmetic encoding is mapped to logarithm domain using add/subtract operations, then computational complexity is reduced, but precision may be affected due to approximations
Solution Approach 1:
The patent uses logarithmic domain representation where arithmetic operations are performed exactly through addition and subtraction of logarithmic values. This approach avoids the precision loss associated with approximations in other methods, as the logarithmic transformation preserves the mathematical relationships needed for precise arithmetic encoding.
Data Source
AI summary
A method and apparatus for performing arithmetic encoding/decoding in an arithmetic encoder is disclosed. It comprises: firstly, when performing binary arithmetic encoding/decoding in the arithmetic encoder, an interval update process for arithmetic encoding/decoding to be performed in the original domain is mapped to the logarithm domain, and the interval update computation is implemented with direct add/subtract operations; during arithmetic encoding/decoding in the logarithm domain, data conversions between the original domain and the logarithm domain are performed by approximations; and after encoding/decoding a symbol, its probability is updated when necessary, the update being performed with add/subtract operations in the logarithm domain. It can be seen that with the arithmetic encoding/decoding solutions of the disclosure, the arithmetic encoding/decoding process and the probability estimation involved therein are mapped to the logarithm domain. Data conversions between the original domain and the logarithm domain are performed by means of approximation equations. Accordingly, complicated computations and table looking-up are avoided effectively. Therefore, the disclosure provides a simple, efficient and suitable solution for performing arithmetic encoding/decoding.